a4-soln

Solving recurrences Solve the following recurrence relations and give a Θbound for eachof them. Do not use the Master Theorem. You must use the recursion tree method. For each recurrence,state the branching factor, the height of the tree, the size of the subproblems at depth k, and the number of subproblems at depth k. You can draw the recursion tree to help find the solution, but do not include the tree in your submission as it will not be graded.(a) T (n) = 4T (n/3)+n(b) T (n) = 3T (n/3)+n(c) T (n) = 4T (n/4)+√n(d) T (n) = 16T (n/4)+n2(e) T (n) = 3T (n/4)+1

Problem 3. Consider the following recurrence. T(n) = {(n) = 37(n T(n) = 3T(n/2) + n² if n=1 otherwise. (a) Solve this recurrence exactly by the method of substitution. You may assume n is a power of 2. (b) Solve it using the recursion tree method.

Solving recurrences Solve the following recurrence relations and give a Θbound for each ofthem. Keep in mind that we’ve seen several examples of how to solve recurrences. You can try to applythe Master’s theorem or use a recursion tree. You can also try to “unfold” the recurrences, as we saw with T (n) = T (n −1) + O(n) in lecture. Another technique is applicable if the work term is not a polynomial: 1) take the polynomial upper bound of it, and see what Master theorem gives you, 2) take the polynomial lower bound of it, and see what Master theorem gives you, and 3) if these agree, then you have an answer.(a) T (n) = 12T (n/5)+13n^1.4(b) T (n) = 6T (n/5)+n^1.3(c) T (n) = 4T (n/2)+log^3 n(d) T (n) = T (n −3)+log n

Question 4 Full explain this question and text typing work only thanks

(b) Solve the recurrence relation : T (n) =T O(n). 3 using the recursion tree method.

Use the recursion tree method to guess tight asymptotic bounds for the recurrence T(n)=4T(n/2)+n. Use substitution method to prove it.

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n)=4T(n/2+2)+n. Use the substitution method to verify your answer.

for the following problem we need to use a recursion tree.  so we can determine an asymptotic upper bound on therecurrence T(n) = 3T(n/2) + n. the substitution method must be used to solve.

Answer the following for the recurrence T(n) = T( n / 2 ) + T( n / 4 ) + n. (a) Use the Recursion Tree method to guess the upper-bound. (b) Prove by induction the upper-bound obtained in the previous question (problem a).

For each of the following recurrences, verify the answer you get by applying the master method, by solving the recurrence algebraically OR applying the recursion tree method.  T(N) = 2T(N-1) + 1 T(N) = 3T(N-1) + n

Use master's theorem and recursion tree.

Please explain Solve the recurrence: T(n)=2T(2/3 n)+n^2.  first by directly adding up the work done in each iteration and then using the Master theorem. Note that this question has two parts (a) Solving IN RECURSION TREE the problem by adding up all the work done (step by step) and (b) using Master Theorem

Problem 3. Use recursion tree to solve the following recurrence. T(n) = T(n/15) +T(n/10) +2T(n/6) + /n

Use a recursion tree to determine a good asymptotic upper bound on the recurrenceT(n) = 3T(n/3) + n.You can assume that n is a power of 3.Show all your work.

Solving recurrences using the Substitution method. Give asymptotic upper and lower bounds for T(n) in each of the following recurrences. Solve using the substitution method. Assume that T(n) is constant n ≤ 2. Make your bounds as tight as possible and justify your answers. Hint: You may use the recursion trees or Master method to make an initial guess and prove it through induction a. T(n) = 2T(n-1) + 1 b. T(n) = 8T(n/2) + n^3

Solve the following recurrence relation. You could use the Master Theorem or any other method seen in class. T(n) = T(n/10) + n²

3) Use recursion Tree to determine a good asymptotic upper bound on the recurrence T(n) = 4T (" + 2) + n Use the substitution method to verify your answer.

2. Find the solution of the following recurrence equation by repeated substitution method, assuming n = 2¹ for some integer i. 1 T(n) = {4T (n/2) + n il if n = 1 ifn ≥ 2 3. Use the recursion tree to find the solution of the following recurrence. T(n)= 4T(n/4) + nª

It is an algorithm problem.

For each of the following recurrences, verify the answer you get by applying the master method, by solving the recurrence algebraically OR applying the recursion tree method.  T(N) = 4T(N/2) + n2logn T(N) = 5T(N/2) + n2/logn

Draw a recursion tree for a recurrence and use the Substitution Method to prove the solution. ( make a sample question )

Part I For each of the following two recurrences, construct a recursion tree and use it to solve the recurrence. Your solution should include a chart similar to examples in lecture and studio with columns for the depth, number of nodes, work per node, and work per level at each level of the tree; a summation giving the total work of the recurrence; and ● a closed-form asymptotic solution to the recurrence. You may assume for simplicity that the input size n is a power of b, the denominator of the size in the recursive term, and that T(1) = d for some constant d. You may hand-draw or typset the chart, but please typeset the summation and its closed-form solution. 1. T(n) = 3T(n/2) + n² 2. T(n) = 4T(n/2) + n²

Solve the recurrence relation

Use a recursion tree to determine a good asymptotic upper bound on therecurrence T(n) = 3T(n/2) + n. Use the substitution method to prove your answer.

This is a question about Divide-and-Conquer Recurrence Equations.  Can you show me the answer with clear explanations for questions a and c? Thank you.